108CHAPTER 2Axially Loaded MembersSolution 2.5-5Bar with nonuniform temperature changeAt distance x:REMOVE THE SUPPORT AT ENDBOF THE BAR:Consider an element dxat a distance xfrom end A.¢T5¢TB¢x3L3≤dd5Elongation of element dxd5elongation of barCOMPRESSIVE FORCEPREQUIRED TO SHORTEN THE BARBY THE AMOUNTdCOMPRESSIVE STRESS IN THE BARsc5PA5Ea(¢TB)4ÊP5EAdL514EAa(¢TB)d5#L0dd5#L0a(¢TB)¢x3L3≤dx514a(¢TB)Ldd5a(¢T)dx5a(¢TB)¢x3L3≤dxLA∆T∆TBBx0LABxdxProblem 2.5-6A plastic bar ACBhaving two different solid circular crosssections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. Thecorresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticityEis 6.0 GPa, and the coefficient of thermal expansion ais 100 3 1026/°C. Thebar is subjected to a uniform temperature increase of 30°C.
This is the end of the preview. Sign up
access the rest of the document.